If the cam/crank sensor is dead the car wont run at all. Could be an intermittent wiring issue with it though, check the CAS and the harness on the passenger side of the head..

Will it stay running if you stay on the gas? Or will it just cut off and die even if you're pressing the gas?

Do you have a CEL? Also, its not the best idea to disconnect the battery while the car is running...if your voltage regulator is less than up to spec it could cause a surge and fry some stuff, fyi.